Skip to main content
SpringerLink
Log in

An Analog of the Fubini–Studi Form for Two-Dimensional Toric Varieties

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

For two-dimensional toric varieties X, an analog of the Fubini–Studi form ω0 is constructed together with the canonical form ω0 that is the kernel of an integral representation for holomorphic functions in d-circular domains in C d connected with two-dimensional toric varieties X. This kernel is shown to be a closed differential form in C d defining the associated positive form ω0 on X.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Griffiths P. and Harris J., Principles of Algebraic Geometry [Russian translation], Mir, Moscow (1982).

    Google Scholar 

  2. Kytmanov A. M., The Bochner-Martinelli Integral and Its Applications [in Russian], Nauka, Novosibirsk (1992).

    Google Scholar 

  3. Shabat B. V., Value Distribution of Holomorphic Mappings [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  4. Audin M., The Topology of Torus Actions on Symplectic Manifolds, Birkhäuser, Boston; Basel; Berlin (1991). (Progr. Math.; 93.)

  5. Cox D., Recent Developments in Toric Geometry [Preprint], Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts (1998).

    Google Scholar 

  6. Cox D., Toric Residues [Preprint], Department of Mathematics and Computer Science, Amherst College, Amherst, Massachusetts (1997).

    Google Scholar 

  7. Batyrev V., “Quantum cohomology rings of toric manifolds,” Journées de Géométrie Algébrique d'Orsay (Juillet 1992), Soc. Math. France, Paris, 1993, pp. 9–34. (Astérisque 218).

    Google Scholar 

  8. Guillemin V., Moment Maps and Combinatorial Invariants of Hamiltonian Tn-Spaces, Birkhäuser, Boston; Basel; Berlin (1994). (Progr. Math.; 122.)

    Google Scholar 

  9. Kytmanov A. A., “The volume form for some toric varieties,” in: Proceedings of the International Conference 'Mathematical Models and the Methods of Their Study,' Krasnoyarsk, IVM SO RAN, 2001, 2, pp. 52–55.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Krasnoyarsk State University, Russia

    A. A. Kytmanov

Authors
  1. A. A. Kytmanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kytmanov, A.A. An Analog of the Fubini–Studi Form for Two-Dimensional Toric Varieties. Siberian Mathematical Journal 44, 286–297 (2003). https://doi.org/10.1023/A:1022936921419

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1022936921419

Search

Navigation